Question

Which of the following is the result of the equation below after completingthe square and factoring?X2+3x+8 = 6O A. (x+2) = -2OB. (x+ 2 - 1OC. (x+3)2 = -2D. (x+3) = 1

Answer 1

Problem:

Which of the following is the result of the equation below after completing the square and factoring?

`x^2+3x+8=6`

Solution:

To complete the square of the polynomial

`ax^2+bx+c=d`

we add to both sides of the above equation the fraction:

`((b)/(2a))^2`

in our case we have that a = 1, b = 3, c = 8 and d = 6 .Then we have that:

`((b)/(2a))^2=\text{ }((3)/(2))^2\text{ }`

adding the above number on both sides of the given polynomial, we obtain:

`x^2+3x+((3)/(2))^2+8=6+((3)/(2))^2`

this is equivalent to:

`x^2+3x+((3)/(2))^2=6+((3)/(2))^2-8`

then we have:

`(x^{}+(3)/(2))^2=(1)/(4)`